On increasing the speed of a train at the rate of 10 km

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On increasing the speed of a train at the rate of 10 km

Home » Aptitude » Speed, Time and Distance » Question

On increasing the speed of a train at the rate of 10 km per hr, 30 minutes is saved in a journey of 100 kms. Find the initial speed of train.

1. 40 kmph
2. 45 kmph
3. 42 kmph
4. 44 kmph

Correct Option: A

Let the original speed be x km/hr
then, increased speed
= (x + 10) km/hr
According to question,
100 − 100 = 30
x x + 10 60

[ ∵ Original time − New time
= 30 minute or 30 hr ]
60

⇒ 100 1 − 1 = 1
x x + 10 2

⇒ x + 10 − x = 1
x(x + 10) 200

⇒ 10 × 200 = x (x + 10)
⇒ x² + 10x – 2000 = 0
⇒ x² + 50x – 40x – 2000 = 0
⇒ x (x + 50) – 40 (x + 50) = 0
⇒ x = – 50, 40
Speed can’t be negative.
Hence, Original speed = 40 kmph